Multiscale challenges

Examination of reported values of diffusion and reaction rate constants point to the inherent multiscale challenges encountered in spatiotemporal modeling of... 

Chu JW, Izveko S, Voth GA. The multiscale challenge for biomolecular systems coarse-grained modeling. Mol. Simulat. 2006 32 211-218. 

The multiscale challenge arises from the recognition that the total gravitational potential associated with an object at a position r relative to the center of the earth... 

A multiscale system where every two constants have very different orders of magnitude is, of course, an idealization. In parametric families of multiscale systems there could appear systems with several constants of the same order. Hence, it is necessary to study effects that appear due to a group of constants of the same order in a multiscale network. The system can have modular structure, with different time scales in different modules, but without separation of times inside modules. We discuss systems with modular structure in Section 7. The full theory of such systems is a challenge for future work, and here we study structure of one module. The elementary modules have to be solvable. That means that the kinetic equations could be solved in explicit analytical form. We give the necessary and sufficient conditions for solvability of reaction networks. These conditions are presented constructively, by algorithm of analysis of the reaction graph. 

Many polymer blends or block polymer melts separate microscopically into complex meso-scale structures. It is a challenge to predict the multiscale structure of polymer systems including phase diagram, morphology evolution of micro-phase separation, density and composition profiles, and molecular conformations in the interfacial region between different phases. The formation mechanism of micro-phase structures for polymer blends or block copolymers essentially roots in a delicate balance between entropic and enthalpic contributions to the Helmholtz energy. Therefore, it is the key to establish a molecular thermodynamic model of the Helmholtz energy considered for those complex meso-scale structures. In this paper, we introduced a theoretical method based on a lattice model developed in this laboratory to study the multi-scale structure of polymer systems. First, a molecular thermodynamic model for uniform polymer system is presented. This model can... 

Glimm and Sharp [307] proposed a challenge to the twenty-first century researcher to consider multiscale materials modeling as a new paradigm in order to realize more accurate predictive capabilities. The context is to predict the macroscale/ structural scale behavior without disregarding the important smaller scale features. 

J.J. De Pablo, W.A. Curtin Multiscale modeling in advanced materials research Challenges, novel methods, and emerging applications. MRS Bulletin 32, 905-909 (2007)... 

Glimm J, Sharp DH Multiscale science A challenge for the twenty-first century. Siam News 30, 1-7 (1997)... 

Maroudas, D., Modeling of radical-surface interactions in the plasma-enhanced chemical vapor deposition of silicon thin films, in (A.K. Chakraborty, Ed.), Molecular Modeling and Theory in Chemical Engineering , vol. 28, p. 252. Academic Press, New York (2001). Maroudas, D. Multiscale modeling, Challenges for the chemical sciences in the 21st century Information and communications report , National Academies, Washington, DC. p. 133. 

On the other hand, the multiphysics, multiscale character of the problem poses formidable challenges for numerical simulation also. The consequence is that practical models are based on judicious decoupling of some parts of the physics. 

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